# Comment on Garc\'ia-Donato et al. (2025) "Model uncertainty and missing data: An objective Bayesian perspective"

## TL;DR

This paper discusses an alternative Bayesian approach for handling missing data in variable selection, using O'Hagan's fractional Bayes factor and Rubin's rules, demonstrating competitive results with prior methods.

## Contribution

It introduces an alternative objective Bayesian method for variable selection with missing data, utilizing fractional Bayes factors and Rubin's rules, and provides a numerical comparison.

## Key findings

- Method shows competitive performance in numerical experiments.
- Utilizes fractional Bayes factor as a Savage-Dickey density ratio.
- Offers a derivation for variable selection with missing data.

## Abstract

Garcia-Donato et al. (2025) present a methodology for handling missing data in a model selection problem using an objective Bayesian approach. The current comment discusses an alternative, existing objective Bayesian method for this problem. First, rather than using the g prior, O'Hagan's fractional Bayes factor (O'Hagan, 1995) is utilized based on a minimal fraction. Second, and more importantly due to the focus on missing data, Rubin's rules for multiple imputation can directly be used as the fractional Bayes factor can be written as a Savage-Dickey density ratio for a variable selection problem. The current comment derives the methodology for a variable selection problem. Moreover, its implied behavior is illustrated in a numerical experiment, showing competitive results as the method of Garcia-Donato et al. (2025).